Well, setting as a feature in a literary work has to do with two things: setting of time and setting of place. This story is quite specific about both.
The setting of time in "Miss Hinch" is generally New York City and specifically on a subway car that is traveling from South 125th Street to 14th Street. (There are also a few interactions at local, New York City businesses such as Miller's Restaurant.) The setting of time in "Miss Hinch" is the early 20th century, after the turn of the century in the 1900s. We can tell that it has to be after the subway system was created in New York City because of the setting of place. The first underground line of the New York City subway was created in 1904, so we can be sure the story takes place after this date.
In conclusion, what we don't really learn from the setting is anything about the two clever women in the story. However, the streets and subway cars of New York City are certainly a pertinent place for these women to play their game of cat and mouse.